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For all integers k the divisibility holds

Source: Baltic Way 2000

December 17, 2010

inductionnumber theory proposednumber theory

Problem Statement

Let

n

be a positive integer not divisible by

2

or

3

. Prove that for all integers

k

, the number

(k+1)^n-k^n-1

is divisible by

k^2+k+1

.

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